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I am currently tasked with calculating the total flux of photons or irradiance from a flat emitter ('pixel'). Previously we measured the Luminance head-on (90 degree from the emitting surface) and calculated the illuminance assuming a lambertian emission. As it turns out the calculation fails for several of our devices because the radiation pattern is very much non-lamberian ($I(\alpha)=I_0*cos(\alpha)$ is not true anymore).

I am now trying to overcome this by measuring the Luminance (lm/sr/m^2) for several angles and integrate it over the solid angle to calculate the full illuminance. However I fail when it comes to the proper discretization of the solid angle.

I attached the equation as I can not write latex here (or can I?) and I am very thankful for any help I can get on this!

I wish you a nice day! Chris

http://imageshack.us/photo/my-images/40/solidanglediscr.png/

(sorry I can not add images due to low reputation!)

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  • $\begingroup$ Latex can be written by enclosing it with dollar signs - one dollar sign at start and end for inline latex, two (start and end) for a latex line centred in page.. e.g. $f(x)$ $\endgroup$
    – geometrikal
    Apr 25 '13 at 5:35
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Google knows:

http://theory.rutgers.edu/~giese/notes/Quadrature.pdf

https://www.mathworks.com/matlabcentral/fileexchange/27097-getlebedevsphere

It's called Lebedev quadrature.

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